FRM- 2 Flashcards
Return on Portfolio of 2 Assets
- Weighted- Average of Returns on Individual Assets
2. Investor to Invest Fully
Standard Deviation of Portfolio of 2 Assets
- Not Weighted- Average of Standard Deviation of Returns on Individual Assets
- Cross- Terms are Involved and Weights Do Not Add to One
Standard Deviation
Volatility of Returns
Delineating
Representing Pictorally
Correlation
+1 To -1
Correlation= +1
- Nothing has been Gained from Diversifying
2. Straight Line in Return- Risk Space
Correlation= -1
- Less Risk
- Positive Investments in Both Assets is Required to Have a Zero- Risk Portfolio
- Graph is Between Risks of Both Securities and Zero- Risk
Power of Diversification of Investments
Reduce Risk
For Correlation Between -1 & +1
- Graph will Lie in the Region Between Straight Line for Correlation +1 & Correlation -1
- Positive Investments
Value of Correlation Can Be Such That
Minimum Risk of Portfolio Cannot Be Less Than the Risk of Least- Risky Asset in the Portfolio
Portfolio Possibility Curve
Curve Along Which All Possible Combinations of Assets Must Lie in Return- Risk Space
Concave Curve
- Higher- Return and Higher- Risk
2. Return of the Portfolio Will Be Greater Than for Same Portfolio With Correlation =+1
Convex Curve
- Higher- Return and Lower- Risk
2. Risk of a Portfolio Will Be Less Than for Same Portfolio With Correlation =+1
Minimum Variance Portfolio
Value of Investment
Combination of Two Portfolios of Same Assets
Is a Portfolio of That Same Assets
In All Possible Combination of All Risk Assets, Investors Look For
- Higher- Return With Same Risk
2. Lower- Risk With Same Return
Efficient Frontier
- Between Global Minimum- Variance Portfolio and Maximum Return Portfolio
- Concave Curve
Short Sale
- Selling a Security Without Owning It
- Borrowing a Security and Selling It
- Borrowing Cost is Same as Expected Return on Security Borrowed or Dividend on the Security If Any
Effect of Short Sale on Efficient Frontier
- No Upper Bound
2. Lower Bound Remains Global Minimum Variance
If Short Sale is Done Using Selling of Security With Higher Return
- Leads to Higher- Risk (Obvious)
2. Leads to Lower- Return Due to a Negative Term in the Equation For Expected Return of Portfolio
Separation Theorem
Ability To Determine the Optimum Portfolio Without Having to Know Anything About The Investor
Rotating the Ray of Efficient Frontier With Risk-less Lending and Borrowing Counter- Clockwise
We Can Get The Tangent to the Efficient Frontier of Portfolio
Beyond Tangent We Cannot Go
- Since Efficient Frontier Shows All Possible Combinations
2. No Line Lies Above the Tangent Line
Considerations In Determining Inputs
- Inflation- Adjusted Inputs
- Input Estimation Uncertainty
- Correlation Over Different Time-Periods
- Short- Horizon and Long- Horizon
Need of Inflation- Adjusted Inputs When
Investment Horizon is Measured Over Decades
T-Bills Are
Partial- Inflation Hedge
Returns Have To Be Adjusted for
Inflation in the Previous Years and in the Coming Years
Historical Analysis Based on Longer Time Period
Is Able To Capture the Changing Pattern in Much More Detail
Characteristics of Security Returns
Changes Over Time
Bayesian Analysis
Variance of Predictive Distribution of Returns
Correlation Also Changes Over Time
- Due to Macro-Economic Conditions
2. E.g. Correlation Between International Market Index
Increase in Inflation Uncertainty
Stock- Bond Correlation Rises
Short Time- Horizon Vs. Long Time- Horizon
- If Returns for Each Year Are Auto-Correlated then Risk Depends Upon Which Time- Horizon is Taken
- E.g. T- Bills
T- Bills Are Auto- Correlated
- Standard Deviation Lower for Lower Time- Horizon
2. No Effect on Return
When Value of X for Which We Get Minimum Variance Portfolio is Positive
It Means Some Combinations of Risky Assets Are Not Efficient
When Value of X for Which We Get Minimum Variance Portfolio is Positive
- It Depends on Correlation
2. Exploits Diversification of Portfolio
Efficient Frontier With Tangent Portfolio
3 Possibilities:
- Risk-Less Borrowing Allowed
- Risk-Less Borrowing Not Allowed
- Risk-Less At A Different Risk- Free Rate
Risk-Less Borrowing Not Allowed
After Tangent, Same As Efficient Portfolio of Risky Assets
Risk-Less At A Different Risk- Free Rate
- Two Points of Tangent
2. Some Portfolios in Which Investors Can Apply Which Are Between Two Tangent Points
